Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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2
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1answer
43 views

$F(x,y)=(x^2,y)$ is not differentiable (According to WA), what am I missing?

Either wolfram alpha is getting crazy or I just completely misunderstood differentiability. Shouldn't it be enough for the partial derivatives to exist and to be continuous? Would the differential not ...
1
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1answer
53 views

Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general?

My question here is pretty basic: Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general? I tried asking WolframAlpha for its solutions, it says that no solutions exist. I ...
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4answers
77 views

$\lim_{z\to1}\frac{1-z^*}{1-z}$ using Wolfram Alpha

I wanted to verify the answer to many questions on limits of complex numbers. So, I tried using Wolfram Alpha for the same. $$\lim_{z\to1}\frac{1-z^*}{1-z}$$ does not exist. [using path $y=m(1-x)$] ...
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0answers
5 views

How to plot a skewed randon numbers on Wolfram Alpha, basically non-linear Ox axis?

I want to see Gauss' bell, but drawn over non-linear Ox axis. Basically i want to visually "catch" some asymetric and very rough plot, that hopefully is just a transformed normal ...
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0answers
20 views

Can Wolframalpha.com display the image of the map $(x,y,z) \rightarrow (x^{2}y,x-z)$?

I can do functions, like $f(x,y,z) = 1$. But is it possible to show the image of this morphism too; $(x,y,z) \rightarrow (x^{2}y,x-z)$?
2
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1answer
81 views

Maximise $(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)})^{\cos x}$

Maximise $$\large \left(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)}\right)^{\cos x}$$ I wonder why Mathematica says infinity as answer, but on desmos graph it is clear that it is less ...
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1answer
62 views

Third vertex of equilateral SPHERICAL triangle

I’m trying to solve Fermat’s problem on sphere for the given triangle ABC using wolfram.I already made out,that in order to find a Fermat’s point i need to build three equilateral triangles on each ...
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0answers
85 views

Wolfram Alpha unknown spooky result for a second derivative evaluated at $\frac 12$. What is the SlowLarge error? [closed]

This is an unexpected short question. Here is the link for this problem. This result should simplify to a π based constant. Here is a photo for this issue: Here is the source for this question: HERE ...
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0answers
26 views

Discrepancy in Wolfram Alpha for the domain of $(\log{x})^{-e^x}$

In my question Question I have discussed in the comments of the domain of $$(\log{x})^{-e^x}$$ In wolfram alpha as matter of fact the domain is $x\geq 1$, but I am not convinced of this fact since ...
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1answer
38 views

How to calculate the constants of the result of a differential equation [closed]

I am trying unsuccesfully to solve this simple problem with Wolfram Alpha given an equation with constants. $$x(t) = c_2 \sin(t w) + c_1 \cos(t w) + \frac{g u}{w^2}$$ I want to calculate the values of ...
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1answer
18 views

Is it possible to use imaginary guesses with secant method?

I was playing with Wolfram Alpha today, and noticed that while I could use, say, $2i$ as a guess to solve $e^x+2=0$ with the help of Newton's method, I couldn't do the same with the secant method. Is ...
1
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1answer
27 views

Does every Matrix have a REF?

I'm wondering if anyone here has experience using Wolframalpha? I can't seem to get a row echelon form (REF) or echelon form, it always does reduced row echelon form (R-REF). Anybody know how to get ...
2
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1answer
66 views

How does WolframAlpha calculate the power of 10 representation of a number? [closed]

Whenever I type some crazy big number on WolframAlpha, it outputs its power of 10 representation. For example, if I input $$ \large e^{6^{3643.23976}}$$ it outputs $$ \large 10^{10^{2834.629359002706}}...
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0answers
50 views

What does this slant “equals” sign indicate in this wolfram alpha plot?

When plotting the function $$\frac{(x^2 -1)}{(x^2 -x -2)}$$ with Wolfram alpha, the second plot has a slant "equals" sign right below when the graph hits the y-axis. What does this indicate? ...
1
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2answers
91 views

Why wolfram doesn't plot the impulses for dirac delta function?

I give wolfram a Fourier transform to solve and I get my answer like this: but when I try to plot it using the plot command like this It doesn't plot the impulses given by the dirac delta function ...
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2answers
55 views

Integral of $\int \frac{\sqrt{a^2-x^2}}{x} \, dx$ and the result of WolframAlpha

In solving the integral $\int \frac{\sqrt{a^2-x^2}}{x} \, dx$ I have found out by hand thet the result is $$|a|\sqrt{1-\bigg(\frac{x}{a}\bigg)^2}+\frac{|a|}{2}\ln\Bigg({\frac{\bigg|1-\sqrt{1-\bigg(\...
1
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1answer
61 views

Is $x$ raised to the power of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ equal to $\begin{bmatrix}x^a&x^b-1\\x^c-1&x^d\end{bmatrix}$?

WolframAlpha says $x$ raised to the power of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ is equal to $\begin{bmatrix}x^a&x^b\\x^c&x^d\end{bmatrix}$. $x = e^{\ln x}$ , and ${x^a}^b = x^{a \...
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0answers
20 views

Equality that does not hold in general for Wolfram Alpha

Why for WolframAlpha $\frac{|\sin(\frac{x}{2})|}{|\cos(\frac{x}{2})|}=\sqrt{\frac{|(1-cos(x))|}{|(1+cos(x))|}}$ is not true $\forall x$? WolframAlpha In my opinion the equality holds since $\sin(\frac{...
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0answers
84 views

Mathematica for computing number and diameter of closed curves in the Riemann Sphere

I am currently learning Python but I don't know (YET!) any language like Mathematica, Matlab, Maple, Octave and so on. I have a Math problem I would like to attack numerically and I need to know which ...
6
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4answers
214 views

Calculating a limit. Is WolframAlpha wrong or am I wrong?

What I'm trying to solve: $$\lim _{x\to -\infty \:}\frac{\left(\sqrt{\left(x^2+14\right)}+x\right)}{\left(\sqrt{\left(x^2-2\right)}+x\right)}$$ What I put into WolframAlpha: ...
1
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1answer
71 views

Closed form expression for eigenvectors of 2x2 matrix?

Is there a closed form expression for the eigenvalues/eigenvectors of an arbitrary 2x2 matrix $ \begin{bmatrix} a & b \\ c & d \end{bmatrix} $? Wolfram|Alpha tries to provide an ...
3
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1answer
27 views

How to count the number of elements needed to get a certain sum?

I want to find $x$ in this equation: $$ \sum_{n=1}^x\left[\left(1- {49\choose6}^{-1}\right)^{n-1} \times {49 \choose 6}^{-1}\right] \geqslant 0.5 $$ If I'm thinking correctly, that's the question of ...
2
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2answers
41 views

Non-converging integral that should be 0

A question requires you to prove that $$\int_0^\infty f(\frac{x}{a}+\frac{a}{x})\frac{\ln{x}}{x}dx=\ln{a}\int_0^\infty f(\frac{x}{a}+\frac{a}{x})\frac{1}{x}dx...........(1)$$ I made the substitution x=...
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1answer
42 views
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1answer
35 views

Continuation of Hypergeometric Function when $a - b$ is natural number

I am currently implementing the 2F1 Gaussian hypergeometric function numerically, and need to know its continuation for $ |z| > 1 $. I have researched this and found this nice formula in the ...
1
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1answer
50 views

How to rewrite 0.ceil(x) in a way that wolfram alpha will accept it

I have been trying to put $0.\lceil{x}$ in wolfram alpha, but it keeps thinking that I am trying to type $0*\lceil{x}$. I've tried experimenting with the idea that when $0<x\le10$, I can write it ...
0
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0answers
29 views

How can I find the expected value and variance of a function using WolframAlpha?

I am struggling to find the expected value (or variance) $E(X)$ of a function using Wolfram Alpha. Writing something like: Find expected value/variance of $f(x)=\frac{1}{e^x}$ for $x$>1 Doesn't ...
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0answers
14 views

Compute closed-form expression for the integral of $-\frac{2x}{x+s}+\frac{x^2}{(x+s)^2}$ against Marchenko-Pastur density

Let $\gamma \in [0,1]$, $s \ge 0$, and define $a:=(1-\sqrt{\gamma})^2$ and $b := (1+\sqrt{\gamma})^2$. For $a \le x \le b$, define $g(x) := -\dfrac{2x}{x+s}+\dfrac{x^2}{(x+s)^2}$ and $f(x) := \dfrac{\...
2
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1answer
39 views

Wolframalpha yields different results of matrix multiplication based on parentheses placement

I was trying to multiply some matrices using wolframalpha when I found that the results didn't match up. Specifically, matrix expression like $CX^2C^{-1}$ produced different result than $CXC^{-1}CXC^{-...
1
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1answer
42 views

What is causing this weird behaviour in Wolfram Alpha, when computing this infinite Sum involving the Zeta function?

This is the Sum: $$\sum\limits_{n=1}^{\infty} \frac{\zeta(2n+1)-1}{\zeta(2n)-1}$$ Sum is divergent, but Wolfram acts weird and after a correct display of early values, it starts converging to a random ...
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2answers
40 views

Finding Nth term using a generating function

Good day everyone I am in need of help, I was using an online program to solve a sequence, the name of the program is WolframAlpha and using it I was able to get the actual nth term that I was looking ...
0
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0answers
37 views

How does WolframAlpha calculate the alternate forms of sin(x)?

I have been searching up the sine of some angles and I noticed that WolframAlpha had some alternate forms that had division and square roots (but only for angles divisible by 3), kind of like sine of ...
0
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2answers
48 views

System of Equation Solver? Online

What site do people use to solve systems of equations with algebraic coefficients. I.E I know wolfram solves $$ x+y=2,~~y-3x=1 $$ but are there sites that let you put unknown constants? $$ x+c_1y=2,~~...
4
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2answers
60 views

Is WolframAlpha wrong on piecewise differentiation at $x=0$?

I'm differentiating the function: $${ f\left(x\right) = \begin{cases}{x \sin ( \frac{1}{x}) } && {x\>\ne\>0} \\ {0} && {x\>=\>0}\end{cases} }$$ In my understanding it is ...
1
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1answer
33 views

Recurrence formula (wolfram alpha error?!)

I tried to identify the simplified reccurence formula for the following function:g(0) = x ; g(n) = g(n - 1) + 1/2 (1 - sqrt(8 g(n - 1) + 1)) But the answer given by wolfram alpha is g(n) = 1/2 n (n + ...
0
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1answer
88 views

Why is Wolfram Alpha showing me this function has no roots; or does it actually have no roots?

I am currently trying to find the roots of this function below. $$ f_s(c,s,\alpha,\rho, \gamma, us) =(\alpha s^{\rho-1} ((1-\alpha)c^\rho + \alpha s^\rho)^{((1-\gamma)/\rho) - 1}) - us $$ , where us ...
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2answers
61 views

Function $\sqrt[5]{x}$

Wolfram alpha tell me that $\lim_{x\to 0-}\frac{\sqrt[5]{x}}{x}$ does not exists and in particular the domain of $\sqrt[5]{x}$ is given by all $x\geq 0$...why? I should say that $\lim_{x\to 0-}\frac{\...
2
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1answer
64 views

Is the solution that Wolfram Alpha gives really the only solution to this problem?

My formula $$(z-y)(z^2+zy+y^2)=(y-x)(y^2+yx+x^2)$$ $$z>=y+2$$ $$y>=x+2$$ $$x>=2$$ I am trying to understand a geometric problem better by plugging my formula into Wolfram Alpha. Normally I ...
0
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1answer
86 views

Why is WolframAlpha and WolframAlpha Widgets Giving me Different Answers?

I was just wondering in anyone's experience, if they came across an official WolframAlpha Calculation (ie. using this https://www.wolframalpha.com/) that was different from one of the widgets (which I ...
0
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1answer
68 views

Why there's a different answer for $\int x\ln{x^2}dx$ in wolfram alpha?

I'm attempting to solve $\int x\ln{x^2}dx$ Using integration by parts I was able to do the following steps. $$2\int x \ln x dx=2\left(\frac{x^2}{2}\ln x -\int\frac{x^2}{2}dx\right)=x^2\ln x - \frac{x^...
7
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1answer
227 views

On an identity that appears in Apéry's proof of the irrationality of $\zeta(3)$

In proving the irrationality of $\displaystyle \zeta(3)=\sum_{n\geq1}\frac{1}{n^3}$, Apéry introduced the accelerated series $$ \zeta(3)=\frac{5}{2} \sum_{k=1}^{\infty}{\frac{ (-1)^{k-1}} {\binom {2k}{...
6
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1answer
107 views

Why do Mathematica and Wolfram|Alpha say $\Gamma(-\infty)=0$?

According to Mathematica and Wolfram|Alpha, $\lim_{x\to -\infty}\Gamma(x)$ is equal to zero. See e.g https://www.wolframalpha.com/input/?i=gamma+function (at the bottom of the page), or try ...
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1answer
64 views

Why Mathematica doesn't evaluate the derivative of the logarithm? [closed]

I'm trying to compute the second-order derivatives of the negative log likelihood as follows: $$ P(t) = \int_{0}^{t}p(v)dv\\ \mathcal{L}(t)=-\eta_n\log\left(1-P(t)\right)\\ $$ Where $P(t)$ is the CDF ...
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2answers
38 views

Is there a way to plot separate functions in 3D using Wolfram Alpha?

Is there a way to plot separate functions in 3D using Wolfram Alpha? Am I doing something wrong? Similar problem with GeoGebra
0
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2answers
53 views

Why are $e^{-4\ln(-x)+4}$ and $e^{-4\ln(-x)}$ positive?

Algebraically, why is $e^{-4\ln(-x)+4}$ a positive result but $e^{-4\ln(-x)}$ a positive result? It seems like with logarithmic properties, they should both be negative, but Wolfram Alpha shows the ...
2
votes
1answer
35 views

Software for evaluating summation expressions involving Stirling numbers of the first kind.

I know that for a summation such as $$p=\sum_{n=o}^{k}{\binom{k}{n}}=2^k,$$ Wolfram Alpha and some other computational software can easily tell that indeed the above summation evaluates to $2^k$. I ...
1
vote
1answer
37 views

Matrix representation after change of basis

I am trying to solve this task using Wolfram Notebook. I would like to know how new matrix is calculated (part b) after a change of basis. Part a: I decided to show this part because part b is a ...
0
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1answer
35 views

Solving a seemingly-trivial trigonometric equation for a specific variable

I'd like to express $y$ in $y = \sin (x*y)$. I can get $x = \frac{\arcsin y} y $ without any issues and then kind of don't know how to continue. WolframAlpha seems to have struggles with the equation ...
2
votes
2answers
49 views

Wolfram: doing substitution on indexed terms

I have sx = Sum[Indexed[x, i], {i, 1, 10}]^2 // Expand It expands in sum of 55 terms, from which $x_i^2$ - 10 terms, actual representation: $x_1^2+x_2^2+x_3^2+...$...
2
votes
2answers
50 views

Equivalent forms for $\int \csc(x) dx$

This question asked about two common forms commonly given for $\int \csc(x) dx$, specifically: $$ (1) \qquad \int \csc(x) dx = \mathbf{{\color{red}-} \ ln|csc(x)+cot(x)| + C}, $$ and $$ (2) \qquad \...

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